This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
What happens when you round these numbers to the nearest whole number?
Find the sum of all three-digit numbers each of whose digits is
Delight your friends with this cunning trick! Can you explain how
Can you explain how this card trick works?
This challenge asks you to imagine a snake coiling on itself.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Here are two kinds of spirals for you to explore. What do you notice?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
This task follows on from Build it Up and takes the ideas into three dimensions!
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
An investigation that gives you the opportunity to make and justify
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Find out what a "fault-free" rectangle is and try to make some of
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?